{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "Attention Mechanism\r\n",
    "==============================\r\n",
    "In this notebook, we introduce the attention mechanism to our plain sequence to sequence model, as illustrated in the diagram below:\r\n",
    "\r\n",
    "![Attention Mechanism](../images/encdec_attn.png)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Download Untility Files for Plotting and Data Generation\r\n",
    "\r\n",
    "Download these utility functions first and place them in the same directory as this notebook. These files are the same as the ones in [Lab11 Sequence to Sequence Model](https://weiliu2k.github.io/CITS4012/LSTM/seq2seq.html)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "from IPython.display import FileLink, FileLinks"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "FileLink('plots.py')"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<a href='plots.py' target='_blank'>plots.py</a><br>"
      ],
      "text/plain": [
       "c:\\Users\\wei\\jupyter_book\\cits4012\\cits4012_natural_language_processing\\cits4012_natural_language_processing\\attention\\plots.py"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "FileLink('plots_seq2seq.py')"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<a href='plots_seq2seq.py' target='_blank'>plots_seq2seq.py</a><br>"
      ],
      "text/plain": [
       "c:\\Users\\wei\\jupyter_book\\cits4012\\cits4012_natural_language_processing\\cits4012_natural_language_processing\\attention\\plots_seq2seq.py"
      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "FileLink('util.py')"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<a href='util.py' target='_blank'>util.py</a><br>"
      ],
      "text/plain": [
       "c:\\Users\\wei\\jupyter_book\\cits4012\\cits4012_natural_language_processing\\cits4012_natural_language_processing\\attention\\util.py"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "FileLink('replay.py')"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<a href='replay.py' target='_blank'>replay.py</a><br>"
      ],
      "text/plain": [
       "c:\\Users\\wei\\jupyter_book\\cits4012\\cits4012_natural_language_processing\\cits4012_natural_language_processing\\attention\\replay.py"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Imports"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "import copy\r\n",
    "import numpy as np\r\n",
    "\r\n",
    "import torch\r\n",
    "import torch.optim as optim\r\n",
    "import torch.nn as nn\r\n",
    "import torch.nn.functional as F\r\n",
    "from torch.utils.data import DataLoader, Dataset, random_split, TensorDataset\r\n",
    "from util import StepByStep\r\n",
    "from plots import *\r\n",
    "from plots_seq2seq import *"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Data Generation\r\n",
    "\r\n",
    "We still make use of the Square Sequences, using the first two corners to predict the last two. Same method as before for generating noisy squares. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "def generate_sequences(n=128, variable_len=False, seed=13):\r\n",
    "    basic_corners = np.array([[-1, -1], [-1, 1], [1, 1], [1, -1]])\r\n",
    "    np.random.seed(seed)\r\n",
    "    bases = np.random.randint(4, size=n)\r\n",
    "    if variable_len:\r\n",
    "        lengths = np.random.randint(3, size=n) + 2\r\n",
    "    else:\r\n",
    "        lengths = [4] * n\r\n",
    "    directions = np.random.randint(2, size=n)\r\n",
    "    points = [basic_corners[[(b + i) % 4 for i in range(4)]][slice(None, None, d*2-1)][:l] + np.random.randn(l, 2) * 0.1 for b, d, l in zip(bases, directions, lengths)]\r\n",
    "    return points, directions"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Plain Encoder-Decoder\r\n",
    "\r\n",
    "We use exactly the same encoder-decoder from Lab11's [sequence to sequence notebook](https://weiliu2k.github.io/CITS4012/LSTM/seq2seq.html)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "class Encoder(nn.Module):\r\n",
    "    def __init__(self, n_features, hidden_dim):\r\n",
    "        super().__init__()\r\n",
    "        self.hidden_dim = hidden_dim\r\n",
    "        self.n_features = n_features\r\n",
    "        self.hidden = None\r\n",
    "        self.basic_rnn = nn.GRU(self.n_features, self.hidden_dim, batch_first=True)\r\n",
    "                \r\n",
    "    def forward(self, X):        \r\n",
    "        rnn_out, self.hidden = self.basic_rnn(X)\r\n",
    "        \r\n",
    "        return rnn_out # N, L, F"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "class Decoder(nn.Module):\r\n",
    "    def __init__(self, n_features, hidden_dim):\r\n",
    "        super().__init__()\r\n",
    "        self.hidden_dim = hidden_dim\r\n",
    "        self.n_features = n_features\r\n",
    "        self.hidden = None\r\n",
    "        self.basic_rnn = nn.GRU(self.n_features, self.hidden_dim, batch_first=True) \r\n",
    "        self.regression = nn.Linear(self.hidden_dim, self.n_features)\r\n",
    "        \r\n",
    "    def init_hidden(self, hidden_seq):\r\n",
    "        # We only need the final hidden state\r\n",
    "        hidden_final = hidden_seq[:, -1:] # N, 1, H\r\n",
    "        # But we need to make it sequence-first\r\n",
    "        self.hidden = hidden_final.permute(1, 0, 2) # 1, N, H                      \r\n",
    "        \r\n",
    "    def forward(self, X):\r\n",
    "        # X is N, 1, F\r\n",
    "        batch_first_output, self.hidden = self.basic_rnn(X, self.hidden) \r\n",
    "        \r\n",
    "        last_output = batch_first_output[:, -1:]\r\n",
    "        out = self.regression(last_output)\r\n",
    "        \r\n",
    "        # N, 1, F\r\n",
    "        return out.view(-1, 1, self.n_features)               "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "class EncoderDecoder(nn.Module):\r\n",
    "    def __init__(self, encoder, decoder, input_len, target_len, teacher_forcing_prob=0.5):\r\n",
    "        super().__init__()\r\n",
    "        self.encoder = encoder\r\n",
    "        self.decoder = decoder\r\n",
    "        self.input_len = input_len\r\n",
    "        self.target_len = target_len\r\n",
    "        self.teacher_forcing_prob = teacher_forcing_prob\r\n",
    "        self.outputs = None\r\n",
    "        \r\n",
    "    def init_outputs(self, batch_size):\r\n",
    "        device = next(self.parameters()).device\r\n",
    "        # N, L (target), F\r\n",
    "        self.outputs = torch.zeros(batch_size, \r\n",
    "                              self.target_len, \r\n",
    "                              self.encoder.n_features).to(device)\r\n",
    "    \r\n",
    "    def store_output(self, i, out):\r\n",
    "        # Stores the output\r\n",
    "        self.outputs[:, i:i+1, :] = out\r\n",
    "        \r\n",
    "    def forward(self, X):               \r\n",
    "        # splits the data in source and target sequences\r\n",
    "        # the target seq will be empty in testing mode\r\n",
    "        # N, L, F\r\n",
    "        source_seq = X[:, :self.input_len, :]\r\n",
    "        target_seq = X[:, self.input_len:, :]\r\n",
    "        self.init_outputs(X.shape[0])        \r\n",
    "        \r\n",
    "        # Encoder expected N, L, F\r\n",
    "        hidden_seq = self.encoder(source_seq)\r\n",
    "        # Output is N, L, H\r\n",
    "        self.decoder.init_hidden(hidden_seq)\r\n",
    "        \r\n",
    "        # The last input of the encoder is also\r\n",
    "        # the first input of the decoder\r\n",
    "        dec_inputs = source_seq[:, -1:, :]\r\n",
    "        \r\n",
    "        # Generates as many outputs as the target length\r\n",
    "        for i in range(self.target_len):\r\n",
    "            # Output of decoder is N, 1, F\r\n",
    "            out = self.decoder(dec_inputs)\r\n",
    "            self.store_output(i, out)\r\n",
    "            \r\n",
    "            prob = self.teacher_forcing_prob\r\n",
    "            # In evaluation/test the target sequence is\r\n",
    "            # unknown, so we cannot use teacher forcing\r\n",
    "            if not self.training:\r\n",
    "                prob = 0\r\n",
    "                \r\n",
    "            # If it is teacher forcing\r\n",
    "            if torch.rand(1) <= prob:\r\n",
    "                # Takes the actual element\r\n",
    "                dec_inputs = target_seq[:, i:i+1, :]\r\n",
    "            else:\r\n",
    "                # Otherwise uses the last predicted output\r\n",
    "                dec_inputs = out\r\n",
    "            \r\n",
    "        return self.outputs"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Attention Mechanism Explained\r\n",
    "\r\n",
    "### An illustration of Attention Scores"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "fig = figure9()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Context Vector\r\n",
    "\r\n",
    "The context vector is the weighted average of encoder hidden states."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "context\\ vector = \\underbrace{\\alpha_0 * h_0}_{alignment\\ vector_0} + \\underbrace{\\alpha_1 * h_1}_{alignment\\ vector_1} = 0.8 * value_{the} + 0.2 *value_{zone}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "But how do we compute alphas - attention scores?"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's use our own sequence-to-sequence problem, and the \"perfect\" square as input to illustrate how the context vector is computed. \r\n",
    "\r\n",
    "A sequence `full_seq` is splitted into source and target sequences. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "full_seq = torch.tensor([[-1, -1], [-1, 1], [1, 1], [1, -1]]).float().view(1, 4, 2)\r\n",
    "source_seq = full_seq[:, :2]\r\n",
    "target_seq = full_seq[:, 2:]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### \"Values\" and \"Keys\"\r\n",
    "The source sequence is the input of the encoder. The hidden states the encoder outputs are going to be both \"values\" (V) and \"keys\" (K):"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "torch.manual_seed(21)\r\n",
    "encoder = Encoder(n_features=2, hidden_dim=2)\r\n",
    "hidden_seq = encoder(source_seq)\r\n",
    "\r\n",
    "values = hidden_seq # N, L, H\r\n",
    "values"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.0832, -0.0356],\n",
       "         [ 0.3105, -0.5263]]], grad_fn=<TransposeBackward1>)"
      ]
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "keys = hidden_seq # N, L, H\r\n",
    "keys"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.0832, -0.0356],\n",
       "         [ 0.3105, -0.5263]]], grad_fn=<TransposeBackward1>)"
      ]
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Query\r\n",
    "\r\n",
    "The encoder-decoder dynamics stay exactly the same: despite that we are sending the entire sequence of hidden states to the decoder, we still use the encoder's final hidden state as the decoder's initial hidden state. \r\n",
    "\r\n",
    "In this example of using the first two corners to predict the last two, we still use the last element of the source sequence as input to the first step of the decoder:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "torch.manual_seed(21)\r\n",
    "decoder = Decoder(n_features=2, hidden_dim=2)\r\n",
    "decoder.init_hidden(hidden_seq)\r\n",
    "\r\n",
    "inputs = source_seq[:, -1:]\r\n",
    "out = decoder(inputs)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The first \"query\" (Q) is the decoder's hidden state (remember, hidden states are\r\n",
    "always sequence-first, so we permute it to batch-first):"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "query = decoder.hidden.permute(1, 0, 2)  # N, 1, H\r\n",
    "query"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.3913, -0.6853]]], grad_fn=<PermuteBackward>)"
      ]
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Compute the Attention Score"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Once we have the \"keys\" and a \"query\", we can compute attention scores (alphas) using them. This is for illustration only, we will progressively develop the `calc_alphas()` to reflect the true processing in the digram.\r\n",
    "\r\n",
    ":::{note}\r\n",
    "The alphas here do not make use of the values of keys and query, they are simply ones averaged by the sequence length.  \r\n",
    ":::"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "def calc_alphas(ks, q):\r\n",
    "    N, L, H = ks.size()\r\n",
    "    alphas = torch.ones(N, 1, L).float() * 1/L\r\n",
    "    return alphas\r\n",
    "\r\n",
    "alphas = calc_alphas(keys, query)\r\n",
    "alphas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[0.5000, 0.5000]]])"
      ]
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We had to make sure alphas had the right shape (N, 1, L) so that, when multiplied by the \"values\" with shape (N, L, H), it will result in a weighted sum of the alignment vectors with shape (N, 1, H). We can use batch matrix multiplication (torch.bmm) for that:\r\n",
    "\r\n",
    "$$(\\textcolor{green}{N}, 1, \\textcolor{red}{L}) \\times (\\textcolor{green}{N}, \\textcolor{red}{L}, H) = (N, 1, H)$$\r\n",
    "\r\n",
    "We can simply ignore the first dimension and PyTorch will go over all the elements in the mini-batch for us.\r\n",
    "\r\n",
    ":::{warning} Why are we spending so much time on shapes and matrix multiplication?\r\n",
    "\r\n",
    "Although it seems a fairly basic topic, getting the shapes and dimensions right is of utmost importance for the correct implementation of an algorithm or technique.\r\n",
    "Worst case is when using the wrong dimensions in an operation, PyTorch *may not raise an explicit error*, causing the almost undetectable Logical Error. This will ultimately damage the model's ability to learn.\r\n",
    ":::"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "# N, 1, L x N, L, H -> 1, L x L, H -> 1, H\r\n",
    "context_vector = torch.bmm(alphas, values)\r\n",
    "context_vector"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.1968, -0.2809]]], grad_fn=<BmmBackward0>)"
      ]
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Once the context vector is ready, we can concatenate it to the \"query\" (the\r\n",
    "decoder's hidden state) and use it as the input for the linear layer that actually\r\n",
    "generates the predicted coordinates:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "concatenated = torch.cat([context_vector, query], axis=-1)\r\n",
    "concatenated"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.1968, -0.2809,  0.3913, -0.6853]]], grad_fn=<CatBackward>)"
      ]
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "In summary, the above can be summarised into the following steps of a typical attention mechanism:\r\n",
    "\r\n",
    "- encoder to get hidden states, which are used as `\"values\"` as well as `\"keys\"`\r\n",
    "- decoder to get the first hidden state, which is used as `\"query\"`\r\n",
    "- query and keys to work out attention scores, `alphas`\r\n",
    "- `\"values\"` weighted by `alphas` to get `alignment vectors`\r\n",
    "- summing up `alignment vectors` to get the `context vector`\r\n",
    "- concatenate `context vector` with the decoder hidden state (in this simplest case, the same as `query`), for output predication.\r\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Scoring Method\r\n",
    "\r\n",
    "In the `calc_alpha()` function above, we used the simple $\\frac{1}{L}$ as weights, which produces an average of the hidden states. Below we show the use of dot product between Q and K as a scoring method. \r\n",
    "\r\n",
    "### Dot product"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "cos\\ \\theta = \\frac{\\sum_i{q_ik_i}}{\\sqrt{\\sum_j{q_j^2}}\\sqrt{\\sum_j{k_j^2}}}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "cos\\ \\theta \\sqrt{\\sum_j{q_j^2}}\\sqrt{\\sum_j{k_j^2}}= \\sum_i{q_ik_i}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "cos \\theta\\ ||Q||\\ ||K|| = Q \\cdot K\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "# N, 1, H x N, H, L -> N, 1, L\r\n",
    "products = torch.bmm(query, keys.permute(0, 2, 1))\r\n",
    "products"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[0.0569, 0.4821]]], grad_fn=<BmmBackward0>)"
      ]
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Attention Scores"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "alphas = F.softmax(products, dim=-1)\r\n",
    "alphas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[0.3953, 0.6047]]], grad_fn=<SoftmaxBackward>)"
      ]
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "source": [
    "def calc_alphas(ks, q):\r\n",
    "    # N, 1, H x N, H, L -> N, 1, L\r\n",
    "    products = torch.bmm(q, ks.permute(0, 2, 1))\r\n",
    "    alphas = F.softmax(products, dim=-1)    \r\n",
    "    return alphas"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Visualizing the Context \r\n",
    "\r\n",
    "Here we use a single query (`q`) and three keys (`k`) to illustrate the idea of using dot products in measuring vector similarity. Visually, the red query vector ($Q$) is closer to $K_0$."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "source": [
    "q = torch.tensor([.55, .95]).view(1, 1, 2) # N, 1, H\r\n",
    "k = torch.tensor([[.65, .2], \r\n",
    "                  [.85, -.4], \r\n",
    "                  [-.95, -.75]]).view(1, 3, 2) # N, L, H"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "fig = query_and_keys(q.squeeze(), k.view(3, 2))"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "\\begin{align*}\r\n",
    "Q \\cdot K_0 = cos \\theta_0\\ ||Q||\\ ||K_0|| =& &0.73 &*& 1.10 &*& 0.68 =& &0.54\r\n",
    "\\\\\r\n",
    "Q \\cdot K_1 = cos \\theta_1\\ ||Q||\\ ||K_1|| =& &0.08 &*& 1.10 &*& 0.94 =& &0.08\r\n",
    "\\\\\r\n",
    "Q \\cdot K_2 = cos \\theta_2\\ ||Q||\\ ||K_2|| =& -&0.93 &*& 1.10 &*& 1.21 =& -&1.23\r\n",
    "\\end{align*}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "source": [
    "# N, 1, H x N, H, L -> N, 1, L\r\n",
    "prod = torch.bmm(q, k.permute(0, 2, 1))\r\n",
    "prod"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.5475,  0.0875, -1.2350]]])"
      ]
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "scores = F.softmax(prod, dim=-1)\r\n",
    "scores"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[0.5557, 0.3508, 0.0935]]])"
      ]
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "source": [
    "v = k\r\n",
    "context = torch.bmm(scores, v)\r\n",
    "context"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.5706, -0.0993]]])"
      ]
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "source": [
    "fig = query_and_keys(q.squeeze(), k.view(3, 2), context)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Scaled Dot \r\n",
    "\r\n",
    "The dot product score is sensitive to the length of the vectors, and we can normalise using the standard deviation, which is roughly the sequare root of the dimension of vector as verified using randomly generated normally distributed data. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Variance of a batch dot product is roughly the same as the dimension of the vector"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "source": [
    "n_dims = 10\r\n",
    "dummy_qs = torch.randn(10000, 1, n_dims)\r\n",
    "dummy_ks = torch.randn(10000, 1, n_dims).permute(0, 2, 1)\r\n",
    "torch.bmm(dummy_qs, dummy_ks).squeeze().var()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor(9.7670)"
      ]
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "Var(Q \\cdot K) = d_q = d_k\r\n",
    "\\\\\r\n",
    "\\sigma(Q \\cdot K) = \\sqrt{d_q} = \\sqrt{d_k}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "source": [
    "dummy_product = torch.tensor([4.0, 1.0])\r\n",
    "F.softmax(dummy_product, dim=-1), F.softmax(100*dummy_product, dim=-1)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(tensor([0.9526, 0.0474]), tensor([1., 0.]))"
      ]
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "scaled\\ dot\\ product = \\frac{Q \\cdot K}{\\sqrt{d_k}}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "source": [
    "scaled_products = products / np.sqrt(2)\r\n",
    "scaled_products"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[0.0403, 0.3409]]], grad_fn=<DivBackward0>)"
      ]
     },
     "metadata": {},
     "execution_count": 32
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "source": [
    "alphas = F.softmax(scaled_products, dim=-1)\r\n",
    "alphas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[0.4254, 0.5746]]], grad_fn=<SoftmaxBackward>)"
      ]
     },
     "metadata": {},
     "execution_count": 33
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "![](../images/aiayn_dot.png)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "source": [
    "def calc_alphas(ks, q):\r\n",
    "    dims = q.size(-1)\r\n",
    "    # N, 1, H x N, H, L -> N, 1, L\r\n",
    "    products = torch.bmm(q, ks.permute(0, 2, 1))\r\n",
    "    scaled_products = products / np.sqrt(dims)\r\n",
    "    alphas = F.softmax(scaled_products, dim=-1)    \r\n",
    "    return alphas"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "alphas = calc_alphas(keys, query)\r\n",
    "# N, 1, L x N, L, H -> 1, L x L, H -> 1, H\r\n",
    "context_vector = torch.bmm(alphas, values)\r\n",
    "context_vector"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ 0.2138, -0.3175]]], grad_fn=<BmmBackward0>)"
      ]
     },
     "metadata": {},
     "execution_count": 35
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Encoder Decoder with Attention Mechanism"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Attention Class"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "source": [
    "class Attention(nn.Module):\r\n",
    "    def __init__(self, hidden_dim, input_dim=None, proj_values=False):\r\n",
    "        super().__init__()\r\n",
    "        self.d_k = hidden_dim\r\n",
    "        self.input_dim = hidden_dim if input_dim is None else input_dim\r\n",
    "        self.proj_values = proj_values\r\n",
    "        # Affine transformations for Q, K, and V\r\n",
    "        self.linear_query = nn.Linear(self.input_dim, hidden_dim)\r\n",
    "        self.linear_key = nn.Linear(self.input_dim, hidden_dim)\r\n",
    "        self.linear_value = nn.Linear(self.input_dim, hidden_dim)\r\n",
    "        self.alphas = None\r\n",
    "                \r\n",
    "    def init_keys(self, keys):\r\n",
    "        self.keys = keys\r\n",
    "        self.proj_keys = self.linear_key(self.keys)\r\n",
    "        self.values = self.linear_value(self.keys) \\\r\n",
    "                      if self.proj_values else self.keys\r\n",
    "                \r\n",
    "    def score_function(self, query):\r\n",
    "        proj_query = self.linear_query(query)\r\n",
    "        # scaled dot product\r\n",
    "        # N, 1, H x N, H, L -> N, 1, L\r\n",
    "        dot_products = torch.bmm(proj_query, self.proj_keys.permute(0, 2, 1))\r\n",
    "        scores =  dot_products / np.sqrt(self.d_k)\r\n",
    "        return scores\r\n",
    "            \r\n",
    "    def forward(self, query, mask=None):\r\n",
    "        # Query is batch-first N, 1, H\r\n",
    "        scores = self.score_function(query) # N, 1, L\r\n",
    "        if mask is not None:\r\n",
    "            scores = scores.masked_fill(mask == 0, -1e9)\r\n",
    "        alphas = F.softmax(scores, dim=-1) # N, 1, L\r\n",
    "        self.alphas = alphas.detach()\r\n",
    "        \r\n",
    "        # N, 1, L x N, L, H -> N, 1, H\r\n",
    "        context = torch.bmm(alphas, self.values)\r\n",
    "        return context"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Source Mask"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "source_seq = torch.tensor([[[-1., 1.], [0., 0.]]])\r\n",
    "# pretend there's an encoder here...\r\n",
    "keys = torch.tensor([[[-.38, .44], [.85, -.05]]])\r\n",
    "query = torch.tensor([[[-1., 1.]]])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "source": [
    "source_mask = (source_seq != 0).all(axis=2).unsqueeze(1)\r\n",
    "source_mask # N, 1, L"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[ True, False]]])"
      ]
     },
     "metadata": {},
     "execution_count": 38
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "source": [
    "torch.manual_seed(11)\r\n",
    "attnh = Attention(2)\r\n",
    "attnh.init_keys(keys)\r\n",
    "\r\n",
    "context = attnh(query, mask=source_mask)\r\n",
    "attnh.alphas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[1., 0.]]])"
      ]
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Decoder with Attention"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "source": [
    "class DecoderAttn(nn.Module):\r\n",
    "    def __init__(self, n_features, hidden_dim):\r\n",
    "        super().__init__()\r\n",
    "        self.hidden_dim = hidden_dim\r\n",
    "        self.n_features = n_features\r\n",
    "        self.hidden = None\r\n",
    "        self.basic_rnn = nn.GRU(self.n_features, self.hidden_dim, batch_first=True) \r\n",
    "        self.attn = Attention(self.hidden_dim)\r\n",
    "        self.regression = nn.Linear(2 * self.hidden_dim, self.n_features)\r\n",
    "        \r\n",
    "    def init_hidden(self, hidden_seq):\r\n",
    "        # the output of the encoder is N, L, H\r\n",
    "        # and init_keys expects batch-first as well\r\n",
    "        self.attn.init_keys(hidden_seq)\r\n",
    "        hidden_final = hidden_seq[:, -1:]\r\n",
    "        self.hidden = hidden_final.permute(1, 0, 2)   # L, N, H                      \r\n",
    "        \r\n",
    "    def forward(self, X, mask=None):\r\n",
    "        # X is N, 1, F\r\n",
    "        batch_first_output, self.hidden = self.basic_rnn(X, self.hidden) \r\n",
    "        \r\n",
    "        query = batch_first_output[:, -1:]\r\n",
    "        # Attention \r\n",
    "        context = self.attn(query, mask=mask)\r\n",
    "        concatenated = torch.cat([context, query], axis=-1)\r\n",
    "        out = self.regression(concatenated)\r\n",
    "        \r\n",
    "        # N, 1, F\r\n",
    "        return out.view(-1, 1, self.n_features)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "source": [
    "full_seq = torch.tensor([[-1, -1], [-1, 1], [1, 1], [1, -1]]).float().view(1, 4, 2)\r\n",
    "source_seq = full_seq[:, :2]\r\n",
    "target_seq = full_seq[:, 2:]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "source": [
    "torch.manual_seed(21)\r\n",
    "encoder = Encoder(n_features=2, hidden_dim=2)\r\n",
    "decoder_attn = DecoderAttn(n_features=2, hidden_dim=2)\r\n",
    "\r\n",
    "# Generates hidden states (keys and values)\r\n",
    "hidden_seq = encoder(source_seq)\r\n",
    "decoder_attn.init_hidden(hidden_seq)\r\n",
    "\r\n",
    "# Target sequence generation\r\n",
    "inputs = source_seq[:, -1:]\r\n",
    "target_len = 2\r\n",
    "for i in range(target_len):\r\n",
    "    out = decoder_attn(inputs)\r\n",
    "    print(f'Output: {out}')    \r\n",
    "    inputs = out"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Output: tensor([[[-0.3555, -0.1220]]], grad_fn=<ViewBackward>)\n",
      "Output: tensor([[[-0.2641, -0.2521]]], grad_fn=<ViewBackward>)\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Encoder + Decoder + Attention"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can safely use the orginal code for grouping the encoder and decoder (in this case, the decoder with attention), and create a valid model, but we would like to store the output to visualise attention scores. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "encdec = EncoderDecoder(encoder, decoder_attn, input_len=2, target_len=2, teacher_forcing_prob=0.0)\r\n",
    "encdec(full_seq)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[-0.3555, -0.1220],\n",
       "         [-0.2641, -0.2521]]], grad_fn=<CopySlices>)"
      ]
     },
     "metadata": {},
     "execution_count": 43
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "source": [
    "class EncoderDecoderAttn(EncoderDecoder):\r\n",
    "    def __init__(self, encoder, decoder, input_len, target_len, teacher_forcing_prob=0.5):\r\n",
    "        super().__init__(encoder, decoder, input_len, target_len, teacher_forcing_prob)\r\n",
    "        self.alphas = None\r\n",
    "        \r\n",
    "    def init_outputs(self, batch_size):\r\n",
    "        device = next(self.parameters()).device\r\n",
    "        # N, L (target), F\r\n",
    "        self.outputs = torch.zeros(batch_size, \r\n",
    "                              self.target_len, \r\n",
    "                              self.encoder.n_features).to(device)\r\n",
    "        # N, L (target), L (source)\r\n",
    "        self.alphas = torch.zeros(batch_size, \r\n",
    "                                  self.target_len, \r\n",
    "                                  self.input_len).to(device)\r\n",
    "        \r\n",
    "    def store_output(self, i, out):\r\n",
    "        # Stores the output\r\n",
    "        self.outputs[:, i:i+1, :] = out\r\n",
    "        self.alphas[:, i:i+1, :] = self.decoder.attn.alphas"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Data Preparation\r\n",
    "\r\n",
    "Training data of the square sequences generated. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "source": [
    "points, directions = generate_sequences()\r\n",
    "full_train = torch.as_tensor(points).float()\r\n",
    "target_train = full_train[:, 2:]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "source": [
    "test_points, test_directions = generate_sequences(seed=19)\r\n",
    "full_test = torch.as_tensor(points).float()\r\n",
    "source_test = full_test[:, :2]\r\n",
    "target_test = full_test[:, 2:]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "source": [
    "train_data = TensorDataset(full_train, target_train)\r\n",
    "test_data = TensorDataset(source_test, target_test)\r\n",
    "\r\n",
    "generator = torch.Generator()\r\n",
    "train_loader = DataLoader(train_data, batch_size=16, shuffle=True, generator=generator)\r\n",
    "test_loader = DataLoader(test_data, batch_size=16)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Model Configuration & Training"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "source": [
    "torch.manual_seed(23)\r\n",
    "encoder = Encoder(n_features=2, hidden_dim=2)\r\n",
    "decoder_attn = DecoderAttn(n_features=2, hidden_dim=2)\r\n",
    "model = EncoderDecoderAttn(encoder, decoder_attn, input_len=2, target_len=2, teacher_forcing_prob=0.5)\r\n",
    "loss = nn.MSELoss()\r\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.01)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "source": [
    "sbs_seq_attn = StepByStep(model, loss, optimizer)\r\n",
    "sbs_seq_attn.set_loaders(train_loader, test_loader)\r\n",
    "sbs_seq_attn.train(100)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "source": [
    "fig = sbs_seq_attn.plot_losses()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Visualizing Predictions"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "source": [
    "fig = sequence_pred(sbs_seq_attn, full_test, test_directions)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x576 with 10 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Visualizing Attention"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "source": [
    "inputs = full_train[:1, :2]\r\n",
    "out = sbs_seq_attn.predict(inputs)\r\n",
    "sbs_seq_attn.model.alphas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[[7.8848e-04, 9.9921e-01],\n",
       "         [1.0210e-02, 9.8979e-01]]], device='cuda:0')"
      ]
     },
     "metadata": {},
     "execution_count": 52
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\n",
    "\\Large\n",
    "\\begin{array}{c|cc}\n",
    "& source\\\\\n",
    "target& \\color{red}{x_0} & \\color{red}{x_1} \\\\\n",
    "\\hline\n",
    " \\color{green}{x_2} & \\alpha_{\\color{green}{2}\\color{red}0} & \\alpha_{{\\color{green}{2}\\color{red}1}} \\\\\n",
    " \\color{green}{x_3} & \\alpha_{\\color{green}{3}\\color{red}0} & \\alpha_{{\\color{green}{3}\\color{red}1}}\n",
    "\\end{array}\n",
    "\\implies\n",
    "\\Large\n",
    "\\begin{array}{c|cc}\n",
    "& source\\\\\n",
    "target& \\color{red}{x_0} & \\color{red}{x_1} \\\\\n",
    "\\hline\n",
    " \\color{green}{x_2} & 0.0011 & 0.9989\\\\\n",
    " \\color{green}{x_3} & 0.0146 & 0.9854\n",
    "\\end{array}\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "source": [
    "inputs = full_train[:10, :2]\r\n",
    "source_labels = ['Point #1', 'Point #2']\r\n",
    "target_labels = ['Point #3', 'Point #4']\r\n",
    "point_labels = [f'{\"Counter-\" if not directions[i] else \"\"}Clockwise\\nPoint #1: {inp[0, 0]:.2f}, {inp[0, 1]:.2f}' for i, inp in enumerate(inputs)]\r\n",
    "fig = plot_attention(model, inputs, point_labels, source_labels, target_labels)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 10 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {
    "scrolled": false
   }
  }
 ],
 "metadata": {
  "orig_nbformat": 4,
  "language_info": {
   "name": "python",
   "version": "3.8.10",
   "mimetype": "text/x-python",
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.8.10 64-bit ('cits4012': conda)"
  },
  "interpreter": {
   "hash": "d990147e05fc0cc60dd3871899a6233eb6a5324c1885ded43d013dc915f7e535"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}